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Izv. RAN. Ser. Mat., 2011, Volume 75, Issue 4, Pages 49–90 (Mi izv4500)  

This article is cited in 6 scientific papers (total in 6 papers)

Factorization semigroups and irreducible components of the Hurwitz space

Vik. S. Kulikov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We introduce a natural structure of a semigroup (isomorphic to the factorization semigroup of the identity in the symmetric group) on the set of irreducible components of the Hurwitz space of coverings of marked degree $d$ of $\mathbb P^1$ of fixed ramification types. We shall prove that this semigroup is finitely presented. We study the problem of when collections of ramification types uniquely determine the corresponding irreducible components of the Hurwitz space. In particular, we give a complete description of the set of irreducible components of the Hurwitz space of three-sheeted coverings of the projective line.

Keywords: semigroup, factorization of an element of a group, irreducible components of the Hurwitz space.

DOI: https://doi.org/10.4213/im4500

Full text: PDF file (759 kB)
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English version:
Izvestiya: Mathematics, 2011, 75:4, 711–748

Bibliographic databases:

Document Type: Article
UDC: 512.53+512.544+512.772.5
MSC: 14H30, 20M50, 57M05
Received: 15.03.2010
Revised: 07.07.2010

Citation: Vik. S. Kulikov, “Factorization semigroups and irreducible components of the Hurwitz space”, Izv. RAN. Ser. Mat., 75:4 (2011), 49–90; Izv. Math., 75:4 (2011), 711–748

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  • https://doi.org/10.4213/im4500
  • http://mi.mathnet.ru/eng/izv/v75/i4/p49

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Vik. S. Kulikov, “Factorization semigroups and irreducible components of the Hurwitz space. II”, Izv. Math., 76:2 (2012), 356–364  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. F. Vetro, “A note on coverings with special fibres and monodromy group $S_{d}$”, Izv. Math., 76:6 (2012), 1110–1115  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Vik. S. Kulikov, “Factorizations in finite groups”, Sb. Math., 204:2 (2013), 237–263  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Vik. S. Kulikov, V. M. Kharlamov, “Covering semigroups”, Izv. Math., 77:3 (2013), 594–626  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. Vetro F., “On the Irreducibility of Hurwitz Spaces of Coverings with an Arbitrary Number of Special Points”, Filomat, 27:8 (2013), 1463–1471  crossref  mathscinet  zmath  isi  scopus
    6. Vetro F., “On Coverings With Special Points and Monodromy Group a Weyl Group of Type B-D”, Filomat, 28:2 (2014), 275–284  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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